The central topic of the summer institute is the mathematical study of nonlinear dispersive equations and of fluid dynamics equations. Although these two subjects can be seen as different, they do have a lot in common. Not only certain equations modeling fluid dynamics are of dispersive type (e.g. various water waves equations), but also a number of techniques are successfully used in both fields. In particular, one can observe in both areas the ever-increasing importance of methods from harmonic analysis. We also note that many mathematicians work simultaneously in both areas. While a number of striking new results were obtained in the past few years, the topic of the summer institute offers an increasing number of challenging problems.
During the summer institute, we will bring together many of the very best specialists of these fields to present the newly developed techniques, review the major recent advances and set up directions for future research.